Determining a warping function between two images is important for several applications. For instance, many projector systems require automatic recovery of the shape of a display surface. There, a known pattern is projected onto a surface having an unknown shape. An image of the pattern on the surface is compared with the known pattern to find the warping function, which manifests the shape of the surface. The warping function minimizes an error between the original and projected images.
Another application is to correct optical distortion of a camera. Distortion can be due to lens distortions, water drops on the lens, distorting glass in front of the lens, or atmospheric conditions.
A number of methods are known for recovering warping functions between images, see, e.g., Uchida et al., “Piecewise Linear Two-Dimensional Warping,” Proceedings of the 15th ICPR, 3, pp. 538-541, 2000. However, that method is limited to linear distortions along a single direction.
Existing non-linear warping recovery methods are computationally demanding because those methods include a 2-D minimization problem, see, e.g., Levin et al., “Dynamic planar warping for optical character recognition,” Proceedings of ICASSP, pp. 149-152, 1992.
Therefore, there is a need for a method that can determine a non-linear warping function between two images that does not have the problems of the prior art methods.